Energy efficiency is an important design paradigm in Wireless Sensor Networks (WSNs) and its consumption in dynamic environment is even more critical. Duty cycling of sensor nodes is used to address the energy consumption problem. However, along with advantages, duty cycle aware networks introduce some complexities like synchronization and latency. Due to their inherent characteristics, many traditional routing protocols show low performance in densely deployed WSNs with duty cycle awareness, when sensor nodes are supposed to have high mobility. In this paper we first present a three messages exchange Lightweight Random Walk Routing (LRWR) protocol and then evaluate its performance in WSNs for routing low data rate packets. Through NS-2 based simulations, we examine the LRWR protocol by comparing it with DYMO, a widely used WSN protocol, in both static and dynamic environments with varying duty cycles, assuming the standard IEEE 802.15.4 in lower layers. Results for the three metrics, that is, reliability, end-to-end delay, and energy consumption, show that LRWR protocol outperforms DYMO in scalability, mobility, and robustness, showing this protocol as a suitable choice in low duty cycle and dense WSNs.